I have mixed feelings here. I am going to give both the positives and negatives with what I see from the email letter and from the little I know, as I am not sure whether they are sincere and want to do better or instead feel no remorse and just worded things in a way they think will reel you back in. I do not know them well enough to say either way, and whether they have done this sort of thing before.
The positive side to me says there is some chance they are trying to do better and understand more, and they sincerely want to listen and admit how they can do better if you or someone else told them more details there. Perhaps that time with you out of their lives and with you showing more distance gave them a different perspective and energy to start being better, knowing they cannot control you anymore.
However, the rational and nitpicking side to me says something seems off with that email, despite the mostly ok words there. I mean, why did they suggest that them invading your privacy was the main issue you were upset at or that caused distance? I mean, why did they not see this email as an opportunity to apologize for other major wrongs that you may have told them about earlier, or that they knew they did was wrong? Why did not they state how they should have done those things differently, or how they can try to make up for those wrongs now?
And why would they jump to wanting you to come to their home, instead of recommending neutral place or asking you to pick the most comfortable method and place for you, but stating only if you ever wanted that? They gave you two options basically, their place or some third party person. They did not ask your feelings there. Also, could talk of them wanting this or that, and being overwhelmed and grieving, be an indicator they are showing they are doing what is best for them and not for you, wanting them to be seen like the victim more later on?
If I were that parent, and if I was sincere in wanting to do better, and to have a new healthier relationship with a grown child, and if I really was feeling remorse for past actions that I knew very much upset them, I would first expressed sincere apology there and blamed myself for messing up there and telling them exactly what I could have done better and should have done instead for each of those things, for all the past things hurtful things, and not just say I was sorry for any recent thing, and not just to say let's talk.
I would validate their pain all those years that I caused,, and I would ask how I could do things better in other ways too, as I have a desire to learn from my wrongs and mistakes, and I would say the goal now is not to raise them, but for them to be happier in life with having less stress and pain from my wrongs. I would tell them of all the things I loved about them, and why I was proud of them. That purpose would not be to get sympathy from them or with intent to increase the odds of further contacts, but so as I could at worst feel like I did the final right thing there, that came from my heart. Granted, selfish or ignorant persons though will have a hard time wording things that way, as the goal could be to say what they think you want to hear, or to reel you in and continue certain selfish and abusive ways.
Whether you give them another chance is your decision. I would just not do it on their terms. If you decide to reply, you can pick the time, method or place, and they should not rush anything, and you can set the terms, like them not playing victim for your choices as an adult, no critiques, no pressure, and you can even be more specific in what you need from them, or else tell them you rather just keep things as they are. I mean, if it were me as the adult child, I think it was a reasonable start for them to say as much as they did, and if you think any future apologies or better treatment towards you from them could much better your emotional health, then it might be worth giving them one more chance by stating like by email what you must see from them, if you feel there is a chance they are sincere in wanting to do better.. But, if you think it is more likely an eventual return to harmful prior ways for them, then it's best to either ignore, or perhaps say like, 'I read your email. I am doing fine with my life. I will contact you per desire or need at my best timing. I wish you well in the meantime.'
I guess though one reason I would not rule out giving them one more chance is it must have been hard for them to say words like we miss you, and to admit they did that recent wrong at least. Narcissists like I know would never word emails like that, or allow someone to send such on their behalf or help them word it like that. The ones I know could not show any sign of sympathy, empathy, wrong, flexibility, open mindedness, or sincerity. So, that gives me some hope in your situation. I can just say in our situations, the patterns of certain adult relative behaviors were so toxic and inflexible we had no choice to end contacts, as they either could not change or admit any wrongs at all, or as promises at changing and to show more care were very short lived.
I do not know your parents well enough though to state what is best for you to do, as I see both sides there. It has to be your choice what you feel could give you the most benefit. In one way, I could say they cannot be trusted yet, as they need to show more, but another side to me says, if you have more empathy and strength than them, consider giving them a final chance, now that they know you have the ability to not deal with them or push them away for longer periods, and since they know they will have to be on their best behaviors.